Online Exercises

Simplex Method with Artificial Variable for Phase I


Below is a java applet that will present a set of linear programming problems for you to solve. You're job is to solve each problem (either by finding an optimal solution or demonstrating that the problem is infeasible or unbounded). After correctly solving a problem, the applet will immediately give you a new one. After you have solved all the problems in the set, press the Submit button to email your score to your instructor (whose email address must be supplied below).

Each problem must be solved using the two-phase Simplex Method with artificial variable x0. Any attempt to make an incorrect pivot will be rejected but your score will be increased by one. Low scores are better than high scores.

The objective has two rows now: the first one is for Phase II and the second one is the artificial variable objective in the auxiliary problem for Phase I. You must click on the appropriate row of the artificial variable column x0 to make the first pivot, generating a feasible dictionary for the auxiliary problem, eliminating all the purple colors in the left column and generating yellow colors in the second row, highlighting the possible entering variables for the auxiliary problem. If the original problem is feasible, you should be able to reduce x0 to zero and make the yellow colors all disappear, and then continue with Phase II as usual.

The set of linear programming problems to be solved is determined by specifying the number of rows, the number of columns, the seed, and the number of problems in the set. Your instructor will tell you what values to use for these fields. Make sure that you enter exactly what your instructor tells you for otherwise you will be doing the wrong set of problems and it will be impossible to fairly evaluate your performance.

Also, be sure to enter your email address and your instructor's email address.

When you are ready to begin, press the Go Pivoting button and then, when the pivot window pops up, press the Start button.

Don't forget that incorrectly pressing one of the termination buttons (Optimal, Infeasible, or Unbounded) counts as an extra pivot, so press these buttons only when you are confident that it is the correct thing to do.

Final note: if for any reason you wish to start over, you may press the Exit button to quit the exam. At that point you can start afresh. Of course, at some time before this online assignment is due you must go to the end and submit a score.

Comment on Usage. If you press the Go Pivoting button twice, then you will get two windows that are initially identical. This is convenient since you can let one window lag behind the other by one iteration and thereby watch your pivots better.